This text is a slightly edited version of lecture notes for a course I gave at ETH, during the Winter term 2000-200f, to undergraduate Mathematics and Physics students. The choice of topics covered here is somewhat arbitrary, and was partly imposed by time limitations. Evidently, these notes do not intend to replace the many existing excellent textbooks on the subject, a few of which are listed in the bibliography, but they might provide a reasonably concise, albeit certainly biased introduction to this huge domain. The approach used here has probably been influenced by my first teacher in Dynamical Systems, Prof. Herve Kunz. I also wish to acknowledge my student's contribution in mercilessly tracking down a substantial amount of typos.